Question: $80$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $80$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 80}$ ${x = 3y-80}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-80}$ for $x$ in the first equation. ${(3y-80)}{+ y = 80}$ Simplify and solve for $y$ $ 3y-80 + y = 80 $ $ 4y-80 = 80 $ $ 4y = 160 $ $ y = \dfrac{160}{4} $ ${y = 40}$ Now that you know ${y = 40}$ , plug it back into ${x = 3y-80}$ to find $x$ ${x = 3}{(40)}{ - 80}$ $x = 120 - 80$ ${x = 40}$ You can also plug ${y = 40}$ into ${x+y = 80}$ and get the same answer for $x$ ${x + }{(40)}{= 80}$ ${x = 40}$ There were $40$ home team fans and $40$ away team fans.